Biomedical Engineering Reference
In-Depth Information
Fig. 1 Two-dimensional
RVE illustrating periodic
boundary conditions, which
can be thought of as
surrounded by identically
shaped RVE's
multi-scale analysis the macroscopic stresses r
macro
and tangent stiffness matrices
4
S
macro
are computed from the microscopic models and supplied to the macro-
scopic integration points. In this case only constitutive equations for the structures
in the RVE have to be available. It will be clear that this method is very expensive,
because of computer time and memory. On the other hand the method is very
suitable for implementation on parallel computers. From the following sections it
will be clear that it is not always necessary to perform a full multi-scale analysis in
the described way.
3 The Role of Heterogeneity in the Stress/Strain State
of Individual Cells
Breuls [
4
] used the multi-level method to study the effect of microstructure on
the load transfer of a macroscopically loaded tissue engineered muscle to the
deformation of single cells. The model described an in vitro experiment that
he performed on Bioartificial Muscles (BAM's). These tissue engineered BAM's
are small strips consisting of a collage/matrigel extracellular matrix (ECM) and
oriented myotubes. This in vitro model system was used in several investigations
to study how cells behave under different loading conditions, by indenting the
strips with a spherical indenter and then follow cell death with vital staining's for
apoptosis and necrosis on a confocal microscope [
5
,
12
,
13
].
Breuls wanted to study the influence of the microstructure on what the cell
''feels'' when the entire construct is loaded. Because the cells in the constructs
formed long myotubes, mostly lying in the direction of the long axis of the con-
struct a two-dimensional plane strain model of the cross section seemed appro-
priate. Micromodel A in Fig.
2
represented the BAM cross section. For
comparison the same analysis was performed on a cross section that was more
similar to real muscle tissue (Micromodel B). Because of symmetry only one
quarter of the cross-section was used for the macroscopic mesh. The mesh con-
sisted of 14 quadratic, rectangular elements with 4 integration points each. In each
Search WWH ::
Custom Search